# A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime - Mathematics > Analysis of PDEs

A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime - Mathematics > Analysis of PDEs - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We derive a criterion for the breakdown of solutions to the Oldroyd-B modelin $\R^3$ in the limit of zero Reynolds number creeping flow. If the initialstress field is in the Sobolev space $H^m$, $m> 5-2$, then either a uniquesolution exists within this space indefinitely, or, at the time where thesolution breaks down, the time integral of the $L^\infty$-norm of the stresstensor must diverge. This result is analogous to the celebratedBeale-Kato-Majda breakdown criterion for the inviscid Eluer equations ofincompressible fluids.

Autor: Raz Kupferman, Claude Mangoubi, Edriss S. Titi

Fuente: https://arxiv.org/